Quantitative Methods A university finance department would like to assess whethe
ID: 3176942 • Letter: Q
Question
Quantitative Methods
A university finance department would like to assess whether travel expenses claimed by members of different departments are significantly different. Having identified two departments that appear to show rather different reimbursement claims, data for these departments over the last calendar year is assessed. Assuming that population expenses are approximately normally distributed, and that population variances are approximately equal, test whether department A’s claims are significantly higher than department B’s claims, at the 5% significance level.
Individual claims department A: 156.67, 169.81, 130.74, 158.86, 146.81, 143.69, 155.38, 170.74, 147.28, 157.58, 179.89, 140.67, 154.78, and 154.86.
Individual claims department B: 108.21, 142.68, 135.92, 109.10, 110.93, 132.91, 127.16, and 124.94.
Explanation / Answer
as population variances are approximately equal ;
from above
hence
degree of freedom =n1+n2-2 =20
and pooled std deviation =((n1-1)s12+(n2-1)s22)/(n1+n2-2))1/2=24.8017
hence std error of mean =sp(1/n1+1/n2)1/2 =10.9922
therefore test stat =(X1-X2)/std error =2.1575
for above at 20 degree of freedom; p value=0.0216
as p vlaue is significantly lower then 0.05 level; hence we reject null hypothesis; and conclude that department A’s claims are significantly higher than department B’s claims
A B 56.67 108.21 169.81 142.68 130.74 135.92 158.86 109.1 146.81 110.93 143.69 132.91 155.38 127.16 170.74 124.94 147.28 157.58 179.89 140.67 154.78 154.86 total 2067.760 991.850 mean 147.697 123.981 std deviation(S) 29.193 13.220